Recently, Lin et al. proposed a new primitive identity-based (IB) homomorphic signature scheme and presented an ingenious implement by using any IB-signature scheme as a building block. In this paper, we consider a new type of attack on their scheme: Related-key attack (RKA) is introduced by Bellare and Kohno in 2003 and widely considered for kinds of cryptographic primitives. Specifically, for the first time, we define the RKA security of IB-homomorphic signature scheme. By modifying the signing secret key as its linear form, we prove that Lin et al.'s IB-homomorphic signature scheme is not RKA secure. But a slight modification of it yields an RKA secure one under the original assumptions. We also present security proof in detail. However, we remark that the reason why RKA on Lin et al.'s scheme can be successful lies in that RKA is outside of its security model. Finally, the numerical analysis and experimental results demonstrate that our modified scheme does not distinctly decrease the computational efficiency of Lin et al.'s scheme.
We prove that the Schrödinger systemwhere n = 1, 2, 3, N 2, λ 1 = λ 2 = · · · = λ N = 1, β ij = β ji > 0 for i, j = 1, . . . , N, has a unique positive solution up to translation if the β ij (i = j) are comparatively large with respect to the β jj . The same conclusion holds if n = 1 and if the β ij (i = j) are comparatively small with respect to the β jj . Moreover, this solution is a ground state in the sense that it has the least energy among all non-zero solutions provided that the β ij (i = j) are comparatively large with respect to the β jj , and it has the least energy among all non-trivial solutions provided that n = 1 and the β ij (i = j) are comparatively small with respect to the β jj . In particular, these conclusions hold if β ij = β (i = j) for some β and either β > max{β 11 , β 22 , . . . , β NN } or n = 1 and 0 < β < min{β 11 , β 22 , . . . , β NN }.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.